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关于方程Z(n2)=φ10(SL(n))的可解性研究
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Abstract:
本文利用伪Smarandache函数、Smarandache LCM函数和广义Euler函数的基本性质，以及一些初等方法和技巧给出φ10(pα)的准确计算公式，其中p是素数，且α是正整数。由此，我们讨论数论函数方程Z(n2)=φ10(SL(n))的可解性，结论是：该方程无正整数解。
This paper applies the basic properties of pseudo-Smarandache, Smarandache LCM and generalized functions, as well as some elementary methods and techniques to obtain an accurate calculation formulaφ10(pα), where p is a prime number andαis a positive integer. Based on this formula, We discuss number- theoretic functional equationsZ(n2)=φ10(SL(n)). It is concluded that there is no positive integer solution to this equation.
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